Question

1º) calcule as raìzes :

a)√1024/256

b)√4096/1296

c)√81/49

2º) calcule as raízes e efetue as operações indicadas:

a)√36/9 - √64/81 + √144/16

b)√225/900 - √400/64 ÷ √1600/576

c) √9/4 × √100/36 + √2500/196

Answer 1

$1)a) \sqrt{ \frac{1024}{256} } = \sqrt{4} = 2$

$b) \sqrt{ \frac{4096}{1296} } = \sqrt{ \frac{256}{81} } = \frac{16}{9}$

$c) \sqrt{ \frac{81}{49} } = \frac{ \sqrt{81} }{ \sqrt{49} } = \frac{ \sqrt{ {9}^{2} } }{ \sqrt{ {7}^{2} } } = \frac{9}{7}$

$2)a) \sqrt{ \frac{36}{9} } - \sqrt{ \frac{64}{81} } + \sqrt{ \frac{144}{16} } \\ \\ \sqrt{4} - \frac{8}{9} + \sqrt{9} \\ \\ 2 - \frac{8}{9} + 3 \\ \\ 5 - \frac{8}{9} = \frac{37}{9}$

$b) \sqrt{ \frac{225}{900} } - \sqrt{ \frac{400}{64} } \div \sqrt{ \frac{1600}{5760} } \\ \\ \sqrt{ \frac{1}{4} } - \sqrt{ \frac{25}{4} } \div \sqrt{ \frac{25}{9} } \\ \\ \frac{1}{2} - \frac{5}{2} \div \frac{5}{3} \\ \\ \frac{1}{2} - \frac{5}{2} \times \frac{3}{5} \\ \\ \frac{1}{2} - \frac{1}{2} \times 3 \\ \\ \frac{1}{2} - \frac{3}{2} = - 1$

$c) \sqrt{ \frac{9}{4} } \times \sqrt{ \frac{100}{36} } + \sqrt{ \frac{2500}{196} } \\ \\ \frac{3}{2} \times \sqrt{ \frac{25}{9} } + \sqrt{ \frac{625}{49} } \\ \\ \frac{3}{2} \times \frac{5}{3} + \frac{25}{7} \\ \\ \frac{1}{2} \times 5 + \frac{25}{7} \\ \\ \frac{5}{2} + \frac{25}{7} = \frac{85}{14}$